Limit Theorems for a Correlated Moving Window Model

A new dependent model for a sequence of moving window variables that has an application in multiple scan statistics is proposed in this paper. In continuation of the existing conditional models, this model seems to be a generalization when the length of a window is greater than one. Moment structure and some basic properties for the model are established. These are used to prove limit theorems for the sums of dependent moving window variables. The central limit theorem is validated using simulation.